Where \(\lambda \)  is the laser wavelength, \(v_{\text{surface}}\)  is the velocity at which the scattering surface is moving, and \(N\)  is the number of times the perturbed surface reflects the light before it recombines with the laser beam again. Studies had been made to locate and mitigate scattering in LIGO [1]}, [2]}. These methods have employed the Hilbert-Huang transform [3]}, a technique for analyzing nonlinear and non-stationary data, consisting of utilizing empirical mode decomposition (EMD) and the Hilbert transform. In Virgo, the time-varying filter EMD (tvf-EMD) [4]} adaptive algorithm was used to improve the scattering's origin localization [5]} and to denoise environmental signals [6]}.
Posteriorly, the scattering characterization, e.g., identifying the reflective surface motion frequency, is necessary to understand how the noise originated. For scattered light characterization, we used pytvfemd, a Python library that implements tvf-EMD [7]}. We show results from the application of the tool on data recorded by the LIGO Livingston detector (LLO) during the third observing run (so called O3). We discuss which areas of the detector and frequencies had a high correlation with the scattering, based on the adopted methodology. Finally, we present gwadaptive_scattering, a new fully automated pipeline based on tvf-EMD to locate and characterize the origin of scattered light glitches as obtained from GravitySpy, a machine learning image recognition tool that classifies transient noise instances (also called triggers) in the strain data [8]}
